JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Trigonometric Equations

More JEE Main questions on Trigonometric Equations

1. Number of solutions of $\sqrt{3}\cos 2\theta +8\cos \theta +3\sqrt{3}=0,\theta \in [-3\pi ,2\pi ]$ is:
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2. The number of elements in the set $\left\{x\in \left[0,180^{\circ }\right]:\tan \left(x+100^{\circ }\right)=\tan \left(x+50^{\circ }\right)\tan x\tan \left(x-50^{\circ }\right)\right\}$ is
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3. Let $S=\{x\in [-\pi ,\pi ]:\sin x(\sin x+\cos x)=a$, $a\in \mathbf{Z}\}$. Then $n(S)$ is equal to :
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4. If $S=\left\{\theta \in [-\pi ,\pi ]:\cos \theta \cos \frac{5\theta }{2}=\cos 7\theta \cos \frac{7\theta }{2}\right\}$, then $\mathrm{n}(\mathrm{S})$ is equal to
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5. Let $\mathrm{S}=\{\theta \in (-2\pi ,2\pi ):\cos \theta +1=\sqrt{3}\sin \theta \}$.
   
   Then ${\sum }_{\theta \in \mathrm{S}}\theta$ is equal to:
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6. The sum of all values of $\theta \in [0,2\pi ]$ satisfying $2{\sin }^2\theta =\cos 2\theta$ and $2{\cos }^2\theta =3\sin \theta$ is
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